The panel discussion workshop will provide information about how to garner financial and other types of support for IBL activities, both from within and from outside your institution. Ideas will include acquiring release time for creating materials and developing courses, describing IBL and its benefits, conducting research on teaching and learning, and seeking potential sources of funding. The workshop will also be an opportunity to network with likeminded members of the IBL community to form partnerships in seeking support and engaging in collaborative work.

Introduction to IBL A mini-workshop with Michael Starbird. Contact Norma Flores if you intend to attend this course

Description

All mathematics departments in the country face the challenges of getting their students to learn to understand mathematics on their own and to be able to produce mathematical ideas. This workshop will assist mathematics faculty members to solve these perennial problems. The workshop will introduce participants to Inquiry Based Learning (IBL) styles of instruction or will augment their skills in student-centered methods of instruction. The workshop will include activities aimed at getting participants to think through the real goals of education and the role that IBL instruction can play in accomplishing those goals for their students. The workshop will be designed for participants who may or may not have had previous experience with IBL techniques. Participants will receive copies of the IBL MAA textbooks Number Theory Through Inquiry (by D. Marshall, E. Odell, and M. Starbird) and Distilling Ideas: An Introduction to Mathematical Thinking (by B. Katz and M. Starbird) and a book describing thinking habits for students and instructors titled The 5 Elements of Effective Thinking (by E. Burger and M. Starbird), and other resource material about IBL.
For faculty members who are unaccustomed to IBL instruction, it is not clear what the role of the faculty member actually is during a typical class day, nor is it clear what the students are supposed to do. We hope to make IBL instruction real for faculty members by showing them several different examples of these methods. The workshop will be valuable for dealing with a range of mathematics courses including mathematics for liberal arts students, calculus, introduction to proof courses, and upper division mathematics courses. We will discuss possible strategies appropriate for courses of different sizes.
The goal of the workshop is for attendees to feel comfortable, confident, and skilled in including IBL methods in the experiences that they give their students in mathematics courses.

The popular refrain “I'm so bad at math I can't even balance my checkbook” is symbolic of society whose mathematical perceptions, beliefs, and abilities are dysfunctional. In our view, a majority of our society has been disfranchised and disempowered. The educational, emotional and economic impacts are profound and disturbing.

Inquiry-based learning (IBL) offers powerful learning opportunities for all students – especially, we believe, for those that have been disengaged and disempowered by the typical approach. At the university level, one of the more representative cohorts of the disfranchised is our general education students. In this workshop, you will actively explore ways in which IBL can have a transformative impact on this audience.

Through classroom videos you get to come inside our classrooms – see students working together, critiquing, inventing, debating, justifying and sharing mathematics – and deconstruct what has nurtured these active pursuits. You will interact with students' mathematical work, their discoveries and their mathematical creations. And you will share in our students' experiences through their journals, songs, poems, artwork and interviews – building new norms for what is possible.

We hope that this experience helps focus attention on the disfranchised and stimulates action on the use of IBL in engaging and empowering them.

In undergraduate proof courses, students primarily observe their instructor's polished and complete proofs and may perceive their instructors as the sole authority to judge the validity of their proof productions. Within such learning environments, undergraduates often view proof as a process that they need to replicate and miss opportunities to negotiate their agreement on the validity of acceptable proofs. In order to support undergraduates in learning proof as a communal, negotiated, and sense-making process, we designed and implemented a series of activities where students constructed arguments, validated others' arguments, used their validations to develop a list of proof-writing criteria, and revised and resubmitted their arguments based on the class-developed criteria. In this way, what “counts” as mathematical proof was determined by the classroom community as a whole, rather than solely by the instructor. In this presentation, we will discuss the results of this instructional sequence, implemented in two content courses and two methods courses at four different institutions, and will provide implications for supporting undergraduates' proof learning as they actively consider what counts as 'proof.'

During this presentation, we will engage participants in validating students' sample arguments to illustrate the structure of our activities and to highlight the potential for reflection on proof-writing criteria. We will also share samples of our students' revisions of their original arguments based on their community-developed criteria.

Mindy Capaldi, What did I do wrong (or right)?

Abstract

From grading participation to giving oral exams, you might be surprised at what worked, and didn't work, in my IBL classes. I compare and contrast IBL strategies used in a 20 student abstract algebra course and four student topology course, and present the success (or not) of those strategies. We will also discuss proposed solutions to the not-so-successful ideas and other unexpected problems that arose.

I will present my strategies, poll participants on whether they think it was successful or not, then discuss what really happened. I will also take the not successful ideas, ask participants to partner and come up with a solution, and then discuss their/my proposed solutions.

David M. Clark, Undergraduate Real Analysis: Designing Course Notes

Abstract

My favorite IBL activity is authoring new IBL course notes in collaboration with colleagues and students. I will present an outline for doing this in the context of a two-semester real analysis course I am now designing. Drafts of notes need to be worked through by students to determine what works best for them. They also need pilot testing by other faculty working through them with their own students. Well vetted and thoroughly revised notes can then be made public and be broadly used.

These particular notes arose as a result of a movement to drop real analysis from our requirements for secondary school teachers because it was too difficult for them. My view was that secondary school mathematics teachers need to have a depth of understanding of the numbers beyond what they themselves will teach directly. But they need it from a course that they can realistically do in an IBL format. I am designing a real analysis course intended to fulfill this goal.

Brian Dorn and Larissa Schroeder, A Tale of Two Calculus classes

Abstract

One
of
the
challenges
of
using
video
in
both
inquiry-based
and
inverted
mathematics
courses
is
providing
ways
for
students
to
actively
engage
with
the
content
while
watching
the
video.
Ideally,
educational
videos
available
to
students
would
not
only
expose
them
to
new
course
content,
but
they
would
serve
as
an
"object
to
think
with"
collaboratively—e.g.,
one
about
which
students
can
converse
to
uncover
shared
misconceptions,
pose
additional
lines
of
inquiry,
or
gain
feedback
from
each
other.
In
this
presentation,
we
will
discuss
a
web-based
media
player,
TrACE,
that
provides
means
for
students
to
asynchronously
pose
questions,
add
comments
and
respond
to
classmates
while
watching
a
video.
In
particular
we
will
present
research
data
from
two
different
implementations
of
TrACE
in
Calculus
1
courses
during
the
2014-2015
academic
year,
giving
particular
emphasis
on
how
instructors'
adoption
of
the
tool
and
pedagogical
approaches
affect
the
quantity,
quality
and
type
of
interactions
between students.
How
session
will
be
active
or
engaging:

As
part
of
the
presentation,
we
will
demonstrate
the
media
player
TrACE.
We
will
provide
time
for
audience
members
to
brainstorm
potential
ways
they
could
incorporate
TrACE
into
their
courses
or
suggest
modifications
to
TrACE
that
would
support
their
teaching.

Chuck Hayward, SupportingInstructors in making the Transition to IBL: Lessons from IBL Workshops

Abstract

Professional development is one way of drawing new instructors into the IBL community. This talk offers insights on how to support faculty and graduate students interested in learning to teach with IBL methods, both informally and through formal professional development activities. Since 2010, five week-long workshops have been held to help instructors learn to implement IBL in their classrooms. Each workshop served between 40 and 55 instructors, who were given pre-workshop, post-workshop, and one-year follow-up surveys to assess the workshop, participants' learning, and participants' instructional practices. The workshops have been effective at helping participants to implement IBL: for the three cohorts for which follow-up data are available, at least 58% of participants reported using at least some IBL methods in the year following the workshop. This talk will share results from the participants' surveys, highlighting the features of effective professional development of IBL practitioners. In addition, 16 past participants were interviewed about their teaching practices and discussed factors that had both helped and hindered their ability to implement IBL in their classrooms, providing lessons on how colleagues can support instructors who are making the transition to IBL.

I will begin the presentation by having small groups discuss and share how they currently develop others (or how they would plan to do so). They will share best practices or ideas for good strategies. Then, we will share and compare our findings from the IBL workshops.

Dorin Dumitrascu, Students' Use of Geometry Axioms to Construct Proofs

Abstract

I present findings from a study on how the undergraduates in a College Geometry course use the axioms of geometry to improve on their mastery of reading and constructing proofs. The course was conducted using the small-group guided discovery method, at a liberal arts college in the Midwest. I will focus on two pedagogical aspects. First I will discuss activities and the special selection of geometry topics that I prepared for guided discovery. I will comment on the effectiveness of this setting in the assimilation of the course content. Then I will assess the proof techniques and the quality of arguments which appeared in the written solutions from the final evaluation of the course. Guided discovery method was a completely new teaching and learning experience for all the students of this study. Their perception of the method will also be discussed.

The participants will experiment with select activities that proved successful in my guided discovery approach to the geometry course.

As a first-timer teaching an IBL course, I taught Discrete Mathematics using a modified-Moore method. I started with existing notes that needed modification to fit the content of the course and I would like to share the lessons that were learned in administering the modified notes in my class. I also gathered other activities and teaching techniques from websites and IBL experts. Some ideas worked great, others worked with some modification and some things that I tried did not work at all. I would like to share the trials, tribulations and the lessons that were learned along the way.

In the Spring of 2013, with the help of an AIBL small grant, course notes for a special topics course titled "Introduction to Graph Labeling" were developed. In this talk we'll work through some of the successful activities from that course and try to find ways to incorporate similar activities into the later part of the course when questions become more difficult. In particular, we might attempt to answer: when focused on solving current research questions in the field, how can we provide enough guidance and "low hanging fruit" so that the students don't stop making progress. Knowledge of graph theory is helpful, but not needed as we try to find ways to make these notes better.

Perry Y.C. Lee and Padraig McLoughlin, Aspects of the Flipped? Inquiry-Based Learning Approach in a “Large” College Algebra Classroom: An Ongoing Report

Abstract

Inquiry-Based Learning (IBL) in a mathematics classroom has been shown to be very effective for engaging students in the understanding of course material. That is, students interact with peers and the instructor by asking questions and conjecturing (by doing mathematics) in the classroom. Recently, the 'flipped' or inverted approach to teaching courses has received considerable attention, and in these flipped courses, students come to class prepared before the class meeting. The common denominator in the flipped and IBL methodologies seems to be an emphasis on student engagement in the classroom.

One author implemented a method which uses both the flipped and the IBL methods (or the F/IBL method) into his 'large' College Algebra classroom during the past Fall 2013 and Spring 2014 semesters for managing and engaging students inside the classroom setting.

During this past 2014 Spring semester, student-learned outcomes were assessed to determine the effectiveness of this F/IBL approach in his large College Algebra classroom compared to two other large College Algebra classrooms that were both taught using the traditional lecture-style methods.
This talk will address the differences in the F/IBL approach used in the Fall 2013 semester versus the Spring 2014 semester; will also present preliminary data of student learned outcomes from the F/IBL and two other College Algebra large classes during the 2014 Spring semester; and what the next phase of this research shall be.

How will this talk be active or engaging?
At the conclusion of the prepared talk, the authors will lead an open discussion about others' experiences (positive and negative) on the flipped IBL methodology and what direction we should take in enhancing student engagement.

Nathaniel Miller, Lee Roberson, Sarah Rozner Haley, and Becky-Anne Dibbs University of Northern Colorado
Panel, Discussion on a Mentoring Program for using IBL Methods in Teaching College Geometry

Abstract

From Fall 2011 until Spring 2014, the Educational Advancement Foundation funded a mentoring program at the University of Northern Colorado in which three mathematics education graduate students were mentored in teaching a College Geometry class using IBL methods. This will be a panel discussion of these three students, Lee Roberson, Sarah Rozner Haley, and Becky-Anne Dibbs, along with their mentor, Nathaniel Miller, discussing this mentoring program and how it has changed their teaching.

Mary Shepherd, A Second Year Perspective on Teaching Abstract Algebra

Abstract

After a “bad” first experience teaching Abstract Algebra last spring (2013), and much soul searching over the summer, I have found an IBL Abstract Algebra book, I like and that fits much closer to my teaching style. I have been using the new book this spring (2014). I will report on both courses and try to share some of the many and daily lightbulb experiences of the students, and some of the difficulties encountered and overcome.

I plan to intersperse into the talk several short activities from my course.

Susan Crook, What's Worked for Me

Abstract

Class preparation can often be a game of “beg, borrow, or steal” as we try to get ready for a number of classes each semester. We all benefit from hearing the experiences of those who have gone before (a technique that can be applied to students in an IBL classroom as well!). In this presentation, I will detail activities and strategies that have worked for me in my full IBL classes as well as those that I sneak into other more traditional classes. I'll also cover some strategies I tried that did not work well and why I think they were not successful.

Victor Piercey, Revising IBL Materials

Abstract

Once you have tried your IBL materials, how do you revise them? In this session, participants will assist in this process by briefly working through a portion of course materials and providing suggestions to the author forimprovement. If time permits, we will identify some common criteria used during this process that may form the beginning of a rubric for the evaluation of IBL materials. The materials come from a course entitled Quantitative Reasoning for Business, which is roughly at the level ofintermediate algebra.

Participants will work through materials in small groups and come up with at least one recommendation for improvement. If time permits, whole group reporting out will involve collecting a list of criteria used during the process which would form a foundation for a rubric for evaluating IBL materials.

Robert Sachs, The Successful First Week of a Flipped Calculus I Course

Abstract

The first week of any course establishes a tone and expectations for the rest of the term. I will report on a carefully designed set of IBL activities that worked well for me this past fall. My context is Calculus I at a research university in an active learning classroom (72 students, 2 learning assistants). The first week established that students would write on the whiteboard walls and share responsibility for their learning. It also got the attention of the large fraction of the class that was calculus-aware. Some data on this experiment will also be presented.

Participants will receive a copy of the course syllabus which includes useful language on IBL. They will critique and improve the materials from the first week and discuss possible student responses.

Lola Thompson, IBL Number Theory (for large values of n)

Abstract

I spent nearly a year planning my first IBL number theory course in exquisite detail, only to wind up with an enrollment that was 2-3 times larger than I was expecting. Rather than abandoning my plans (and teaching a standard course with lectures and textbooks), I decided to make a number of last-minute adjustments. In this talk, I will discuss some time-saving (and sanity-preserving) techniques for using IBL in a larger-than-expected course. Topics include: structuring and evaluating group homework assignments, managing student presentations in larger classes, and fostering a productive collaborative environment in a tightly-packed lecture hall.

I will model the way that I run my class by giving participants worksheets and breaking them into groups. I will ask participants to solve an "exploratory" problem and then I'll demonstrate how I motivate my students to make good conjectures and build up to more difficult concepts.

4:15 – 5:15 Themed Parallel Sessions

Melvyn Jeter, An Important Aspect of the Moore Method

Abstract

An important aspect of the Moore Method is to develop within each student the confidence that he or she can create mathematics and effecively communicate it to colleagues in clear writen and verbal form. Requiring students to work on challenging problems that may take an extended period of time to solve is a vital part of this process.The most important thing that students often take from their Moore classes is the ability to work on challenging problems, eventually solving some of them, and possessing the ability to successfully present the solutions to their peers. We are constantly told this by our graduates.

I hope to have Karl Pierburg who is the Senior Director for Football Systems for the Atlanta Falcons attend the meeting to explain how his experience in Topology at Illinois Wesleyan University provided him with the skills that has lead to his success with the NFL.

Michael Gagliardo, Taxi Cab Circles

Abstract

This session on Taxi Cab Geometry will follow an activity I have used in class and during a Math Teachers' Circle. Participants will first gain some experience dealing with the taxicab metric before they are tasked with creating and exploring their own conjectures. Due to most peoples' familiarity with Euclidean geometry, this activity has been successful at introducing a variety of audiences to creating conjectures and has even produced the topic of a Masters' thesis.

The participants will get hands on experience creating circles and lines using the taxi cab metric and will then spend time creating and proving various conjectures about taxi cab geometry.

Matthias Kawski, IBL experiments in the MathCircle at ASU Tempe

Abstract

Given the special demographics and ASU being the only research university
university in the Phoenix metro area (compare Boston or SanFrancisco),
the MathCircle at ASU Tempe uses its locally singular resource, research faculty,
to meet the needs of students who need more math than schools and
community colleges can deliver.

Our focus is, as far as feasible, to start with problem settings that
are meaningful to even advanced middle school students, and which ideally
show a line that connects with cutting edge research, even Abel or Nobel
prizes (e.g., network sorting, stable marriage problem).

Some session leaders use the MathCircles for teaching experiments
that we are not quite ready to try in our regular college classes.
In contrast to common exercises or competition problems, we prefer
problems that are not quickly finished with a period at the end.
Instead the highest premium earn open-ended problems for which
each answer makes the student participants ask more questions,
and which ideally open up entire lines of inquiry and research.
An important goal is to develop a culture of inquiry in which
it is normal to not get an answer in minutes, but instead
convey that this working like a real mathematician!

We plan that for a portion of the session, participants engage
as if they were participants in a typical MathCircle session,
and then have participants reflect on their learning experience,
and how this may be different from traditional learning environments.

MathILy (short for "serious Mathematics Infused with Levity") is an intensive residential summer program for mathematically talented high-school students. IBL is integral to MathILy culture and practice. We use IBL with potential students starting with the Exam Assessing Readiness, which reaches about 10 times as many students as participate in MathILy. (We will share a copy of this year's EAR with conference attendees.) As a way of simultaneously doing outreach and recruiting for MathILy, staff run activities for attendees at some math competitions.

The bulk of MathILy itself is inquiry-based classes, run without textbooks and also without worksheets or other pre-prepared guidance for inquiry. In this session we will describe the techniques we use to frame, encourage, and guide inquiry at MathILy, and we will invite fellow conference attendees to participate in a live demonstration of a bit of a typical MathILy Root Class meeting. Of course, we will also share a description of (and Q&A about) the structure of MathILy and process of MathILy admissions. Finally, we will describe how the MathILy approach to IBL can translate into college courses for mathematics majors.

The idea of mixing IBL methods and flipped classroom approach came to me as I was talking to a high school teacher in town. I was directed to a collaborative research project that was written by two high school teachers for grade 9 students in a Humanities class. At the beginning it was not very clear to me how I could try and still be effective for my students in learning mathematics. I was not sure if I could actually implement this allignment. After contemplating it with fellow mathematicians I decided to give it try in a Pre-Calculus course. This presentation will highlight the experiences gained and the lessons learned by both of us (students and myself).

Regina
Jackson, Michel
Smith,
Teaching
teachers to
teach with IBL

Abstract

With the increased interest in the Common Core and the implementation of Common Core standards by many states comes the opportunity to encourage expanded use of the IBL in the K-12 classrooms. A program is being considered at Auburn whereby Elementary Teachers can obtain "certification" in Mathematics for Elementary Education as part of a graduate program for teachers pursuing Masters Degrees. Techniques of IBL have been modeled in a course for students in this program. As part of professional development, Middle School and High School teachers from lower Alabama attend summer workshops hosted by Troy-Dothan. IBL techniques are modeled in an intensive day-long workshop. A sampling of models from these programs will be presented.

Inquiry-based learning can be employed as a tool to challenge existing knowledge, beliefs, and practices of K-12 teachers. Research shows that professional development focused only on new material and changing a limited number of teaching practices will often result in teachers adopting only those ideas and skills that fit within their existing framework of teaching knowledge and practice. In order for one to be open to new ideas and new ways of doing things, it may be necessary to confront existing beliefs and practices by establishing cognitive dissonance, the feeling of discomfort a person experiences when presented with conflicting ideas or knowledge. If teachers are provided with sufficient time and support to work through any dissonance that they have experienced, they may be open to a transformation of their beliefs and practices. IBL creates an environment for transformative learning provided there is time and support for teacher to think through any dissonance that they have experienced and thus developnew beliefs and practices that fit with their new understanding. We will present evidence that IBL can be an important tool in training K­12 teachers, especially those teachers who are assuming a role of leadership.

Daniel Kiteck, An IBL Approach to Abstract Algebra

Abstract

I taught a lecture-based Abstract Algebra class for three consecutive years. With less than satisfying results, I needed a new teaching method. I found a middle ground between lecture and the traditional Moore Method that I have now used the last two years. One of my primary goals is for my students to develop a deep understanding of proofs for an introduction to groups and rings. (I use the first half of Gallian's “Contemporary Abstract Algebra.”) To accomplish this goal, the vast majority of each class time consists of students presenting the material, asking questions, and helping each other with understanding. No student knows beforehand who I will call, so all of the students prepare for all of the material. A single student is responsible for a presentation, but another student also stands at the front acting as a “support person” for encouragement and as a resource. When needed, I provide probing questions and connections. I see vast improvement in every way, from deeper questions from the students to better student evaluations.

12:00 – 1:15 Lunch. Speaker: Karen Saxe, Creating a Common Vision for the Undergraduate Math Program in 2025

Abstract

The mathematical sciences community is at a pivotal point. Politicians across the country and mathematicians throughout our community, not just mathematics educators, seem to be more keenly focused on undergraduate mathematics education issues than in the past. In order to capitalize on the current climate, the MAA is partnering with other professional societies to consider how we might modernize our curricula and programs to better prepare students for the demands of the 21st century workplace. We have a window of opportunity to catalyze widespread adoption of curricula and pedagogies that are geared toward the development of a broad base of intellectual skills and competencies that better prepare students for the workforce, and are simultaneously endorsed by a broad cross-section of the mathematical community.

We have undertaken an initiative to bring stakeholders in the mathematics education enterprise together to reconsider our long-standing traditions, both curricular and pedagogical. The primary goal of this initiative is to develop a shared vision of the need to modernize the undergraduate mathematics curriculum, especially the first two years, a vision that a core group of professional societies can endorse and promulgate, and about which the societies have some degree of confidence that a broad cross-section of the community will embrace. In this talk, we will share more details about the initiative and where we are in the process.

Process Oriented Guided Inquiry Learning (POGIL) is a student-centered teaching method that provides students with the tools to construct new knowledge and has been used in chemistry since 1994. In POGIL, students are broken into groups of four. The groups are provided with a carefully designed activity that guides them through core concepts. POGIL develops problem solving skills, critical thinking skills as well as a deeper understanding of the material. To ensure all students are actively engaged each student is made responsible for a specific task. Typical POGIL activities include very little lecture and are usually timed. My introductory classes often include non-STEM majors who find it difficult to learn under time constraints and without lecture. To serve these students, I have developed my own style of POGIL involving the following three components:

Mini Lecture

POGIL Activity

Wrap-Up Lecture/Mini Quiz

In this talk I will be presenting the inquiry-based method that I use in a chemistry classroom containing STEM and non-STEM majors. Currently this IBL technique is used in a variety of disciplines and in many high schools and colleges. Like many other IBL methods, POGIL can be adapted for use in virtually any STEM field.

Suzanne Doree, The Coins go “round 'n 'round

Abstract

Take a number of coins and arrange them in piles. Now remove the top coin from each pile and form a new pile out of those collected coins. Repeat. What happens? This seemingly simple (and seemingly endless) process, first popularized by Martin Gardner in a 1983 article, leads naturally to many questions for students to explore. This session will allow attendees to participate (as students) in this classroom-tested activity; to uncover the learning objectives of the lesson; and to experience the pedagogical strategies employed. The lesson has been used in a sophomore level discrete mathematics (introduction to proofs course) and with high school mathematics teachers. The questions connect to graph theory, number theory, and dynamical systems — if I say any more it will spoil the mathematical surprises.

Participants will receive a copy of the activity, instructor notes, and bibliography which appear as a chapter I wrote for MAA Notes #74 Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles, edited by Brian Hopkins (2009). Part of my motivation for this session is to make more IBL folks aware of this useful resource. But mainly, it's just my favorite IBL activity.

Harold Reiter, Teaching PIE to 10-Years Olds

Abstract

Understanding the principle of Inclusion/Exclusion does not depend on a solid foundation of algebra.
I plan to show how we can use a collection of wooden cubes to introduce algebraic ideas and to understand some fundamental relationships between algebra and geometry. I've used this idea for each of the last 6 summers at math camps for students as young as nine.

Larissa Schroeder, Is \(D_x f(g(x)) = f^\prime (g(x))\)?

Abstract

This activity is a graphical exploration of the derivatives of composite functions. It is implemented prior to the formal introduction to and statement of chain rule in an inverted Calculus I course. The functions in this activity provide students with a concrete and accessible set of counterexamples demonstrating that the derivative of \(f(g(x))\) is not equal to \(f^\prime (g(x))\). The activity begins with a true or false classroom voting question: \(\frac{d}{dx} \sin(8x) = \cos(8x)\). Students then use the app PocketCAS on class iPads to compare and contrast the derivative graphs for sine and cosine functions of the form \(y = \sin(ax)\) and \(y = \cos(ax)\) for \(a > 0\). PocketCAS allows the students to graph the derivative without finding its equation. Finally, students make and test hypotheses about derivatives of functions such as \(y = \sin(ax \pm b)\) or \(y = \cos(ax^2 \pm b)\).

How the session will be active and engaging for participants:
The session will begin with the classroom voting question. Participants will have an opportunity to complete the investigation using personal technology. Time will be provided for a discussion around how this activity might help students with their understanding of the chain rule and/or possible modifications.

David Crombecque, Models for Multiplication and Division: An IBL Activity for Pre-Service Teachers

Abstract

In a collaboration between the USC Rossier School of Education and the
Mathematics Department, we have developed a class called The
Foundations of Mathematics and the Acquisition of Mathematical
Knowledge.
Every topic is covered using IBL activities. During class, students are given
a set of creative activities.They then report on their results followed by a
discussion. By the end of each session, students have developed on their
own mathematical models and definitions of the concept in question. The
class targets pre-service K1 through 12 teachers and takes a closer look at
K-12 mathematics and the learning process specific to Mathematics.
Through the semester, students will be encouraged to "adopt the habits of
mind of a mathematical thinker and problem solver including reasoning and
explaining, modeling, identifying structure, and generalizing" (quote from
The Mathematical Education of Teachers).
Pre-service teachers taking this class spend an entire semester rediscovering
K12 mathematics through IBL while also practicing IBL activities they will
be able to use in their own classrooms.

In this presentation, we present an update on a three-year investigation into the concerns and challenges instructors report facing as they implement inquiry-based learning [IBL] methods in undergraduate mathematics courses. Through an online survey, instructors completed bi-weekly logs to report about concerns on eleven aspects of their teaching: class preparation, designing assessment, homework, large group discussions, small group work, lecturing, mathematical content, assessment, student difficulties, and student presentations, and any other concerns that do not fit these categories. We use logs completed over a period of two years by 54 instructors who had different levels of expertise with the IBL method and taught different types of courses. Using constant comparative analysis of these log entries, we have identified several areas of concerns that cut across the different aspects of IBL teaching (e.g., students' resistance to IBL, limitation in available resources) and some that are particular to the different teaching strategies teachers use (e.g., managing group work, dealing with student engagement). In addition we contrast these concerns by instructors' level of expertise with IBL and by the type of courses they were teaching.

Alessandra Pantano, Embracing beauty: Learning symmetry through art in grade school and beyond

Abstract

This workshop is devoted to a mathematical exploration of the isometries that preserve a beautiful periodic pattern, and how they can be combined to form a wallpaper group. (Surprisingly enough, only a very limited number of groups of symmetries exist.)
Different questions can be posed, depending on the age of the participants. Middle schoolers may be asked to find a smallest region that generates the entire pattern under translations, and to identify all the elements of symmetry within this tile (rotocenters, mirror lines, lines of glide reflection). High schoolers may be challenged to find an even smaller region that generates the entire pattern using all the symmetries, and to think about the orbifold that results from gluing together the boundaries of the unit cell that are identified by the symmetries. Mathematics majors can be guided through the task of identifying which of the 17 possible wallpaper groups arises from a given periodic pattern.
In each case, groups of students carry on the mathematical investigation on art work printed on poster size paper. The instructor may guide the discussion through a slide presentation, showing the students how to perform similar tasks on one of the beautiful Escher's periodic drawings.

Brian Bowen, Building Our Conceptual Understanding of Formulas for Volume

Abstract

For several semesters I have taught geometry class designed for pre-service middle grades mathematics teachers (PSTs). During this time an issue that has continued to surface is the way in which these PSTs speak about their past experiences learning mathematics during their middle grades experience. For many, the use of rote memorization was often the primary way in which content was conveyed from teacher to student. For example, when the PSTs were asked to describe the way in which they learned formulas related to volume many described being “handed a piece of paper and told to memorize.” Research suggests that these experiences may not only have a negative effect on the mathematical knowledge held by the PSTs, but also on the pedagogical approaches they will choose once they themselves become classroom teachers.

In response to the disjointed knowledge of volume held by the PSTs I have established series of inquiry based lessons that use concrete learning experiences to discover connections between the volumes of the figures. Discovering these connections allowed the PSTs to derive the formulas, building conceptual knowledge of content that was prior relegated to memorization.

Participants of the session will engage in two activities comparing the relative volume of cylinders to cones and cylinder to spheres. We will use these comparisons to make sense of the traditional formulas for the volume of cones and spheres

Mathematics is a cumulative discipline and the mathematics taught at the middle and secondary levels and in college is based on the mathematics learned in the elementary grades. The role of the elementary teacher, therefore, is of paramount importance in laying the foundation for success in later mathematics courses and instilling in the student a love of mathematics that may later translate into a scientific or technological career. Unfortunately the vast majority of elementary teachers are ill-prepared in and fearful of mathematics, and do not find teaching mathematics a pleasant experience.

The Vermont Mathematics Initiative (VMI) is a highly successful statewide program that trains elementary teachers to be mathematic leaders in their schools. This presentation focuses on the inquiry based instructional strategies developed and employed by VMI which are instrumental is transforming mathphobic teachers into strong mathematical thinkers who view themselves as mathematicians, view mathematics as part of their lives, see the world around them in a mathematical light, and are enthusiastic about teaching mathematics.

John Paul Cook, Bran Katz, Milos Savic, Guided Reinvention of Rings

Abstract

We are developing classroom materials that support students as they reinvent basic definitions from ring theory and explore the challenging concepts in this new mathematical setting. These materials elicit fascinating student thinking, and they are carefully designed to leverage that thinking. In this talk, we will discuss pivotal moments in the students' reinvention process. This project is part of a larger project at the intersection of IBL and RUME (research in undergraduate mathematics education).

The author took 11 courses from RL Moore in the 1960s before receiving his
PhD under RH Bing. In reporting his personal observations, this presentation will
discuss teaching methods depending upon the particular goals of the class in which
they are to be used. Such goals may be (1) practical goals for engineers and applied
mathematicians; (2) in depth goals which emphasize the underlying theories; and (3) a
general history goal. Classes in each of these categories should be taught in a different
manner. In the author's experience, there is much discussion about the best teaching
techniques to get students from point A to point B, but not enough discussion in the first
place about where point B is or should be.
The above three goals apply to any discipline or department. But only in
mathematics is there a fourth category — (4) teaching precise thinking. Moore's method was solely related to this last category. Moore believed the importance of a
mathematics class was not the goal, but the journey. And the journey was to get his
students to think for themselves, deeply and precisely. The presentation will discuss
his methods to accomplish this. They were somewhat different from today's IBL.

Brad Bailey, How Much 'Moore' Do My Students Want?

Abstract

In this talk we will describe a style of Modified-Moore Method (MMM) used at our institution in Precalculus classes as part of a two-year research project to study the impact of such inquiry-based practices on students' performance, and students' attitudes about mathematics and the learning of mathematics. Varieties of both quantitative and qualitative methods were used to measure and study these impacts. One of the instructors involved in the study will briefly describe our teaching method, including highlighting some ways in which it differs from Dr. Moore's original method and provide some rationales for these departures. We will briefly detail the daily classroom activities—meaning what the students and the instructor did on a typical day. After describing the teaching style and the instruments used to study its effects, we will share preliminary results from both the qualitative and quantitative components of the study. Though the data analysis is on-going, the results thus-far indicate that the MMM students tended to have higher achievement on some measures, but also tended to prefer direct instruction. We will share ideas for new directions of study based on our finding. (This research is funded by a grant from the Education Advancement Foundation.)

Wayne Tarrant, Taking IBL to new communities

Abstract

Most of us have taught a point-set topology, introduction to proofs, or real analysis course using IBL, and this is a great thing. I submit that we can take IBL to colleagues beyond mathematics in order to enrich student learning and experiences in more areas. When I encourage students to be as active in other classes as they are in mine, I have run into trouble with a few colleagues for such meddling. And this is an opportunity to have dialogue with colleagues.

I have run a semester-long workshop on IBL for an entire undergraduate faculty and attempted IBL teaching in Paris, both thanks to support from AIBL. In addition I have taught MBA courses using IBL, introduced IBL to some in the homeschooling community, and now use IBL at an undergraduate science and engineering college, among many other attempts. Each of these endeavors has had varying degrees of success, but every instance has given its own lessons.
In this talk I will recount my experiences. I will admit my failures and speak of what has worked. I am hopeful that someone will learn from my tries and will decide to spread IBL to new audiences.

External expectations for "coverage" and the necessity of making courses fairly similar between sections taught by different people can make it hard to do as much inquiry-based pedagogy as many of us would like. Perhaps nowhere is that more true than in calculus, with its many campus constituencies. It can be especially challenging to use IBL techniques only on a replacement basis while sticking with a typical text.

The time of introducing new concepts (like the derivative and integral) is one place to start trying to do so, because many standard curricula now take extra time for this. This session will introduce various IBL "drop-in" activities used successfully as group work over five years in a one-semester applied calculus course in such a context. Participants will get the chance to pretend they are the students, as well as to discuss what concepts might fruitfully be introduced with this sort of approach.

Yun Lu, Projects for calculus classes

Abstract

During this talk, I want to share my experience of using projects to enhance students' learning in my calculus class of the previous semester. I will talk about my motivation, problems encountered, success received, as well as students' feedback. I would also like to get some suggestions and comments from the audience about more techniques that I may use for my future teaching.

Much of learning no longer takes place in a common classroom with a chalkboard. To better engage the new generation of students in inquiry-based learning, the integration of simple technology tools can help meet student needs in a variety of content areas. Being that IBL is student-centered, we want to show how to put the technology in the students' hands. Students involved in critical thinking can utilize free online support tools to help them express themselves and the ideas they form in their minds. Students need to be able to communicate their thinking to others and collaborate with each other, as well as experts, to help them problem solve. When the students can easily communicate with others, reliance on the instructor lessens. Free online technology tools (e.g., concept maps, blogs, wikis, social bookmarks, and polling/survey, whiteboards, website creation) can help facilitate different implementations of IBL. We would like to discuss and demonstrate some easy ways to implement Web 2.0 tools into your IBL. Each phase of IBL can use different tools. No matter how many phases or how you label them, technology can be utilized to enhance your IBL classroom, make it more efficient, and more effective.

Audience participation will include interacting with online tools and the discussion presentation by utilizing personal devices (smart phones, iPads, laptops). Some of the specific tools we can discuss are Diigo, Google docs, Polleverywhere.com, Gliffy, and more. Devices with Internet connection will be useful for audience participation during this presentation.

University of Nebraska--Lincoln's Department of Mathematics has been offering courses for teachers for professional development or for pursuing an advanced degree with a focus on mathematics education. The face-to-face sections of these courses are highly interactive, with participants working in groups on problems during class time and sharing/discussing different solution strategies as a whole class. This presentation will discuss how these features of the in-person course have been transferred to an online setting. The successes and challenges of various approaches to address course features will be shared, and will include feedback from teachers enrolled in the past sections of the courses.

J.C. Price, Transforming Calculus with Technology and IBL

Abstract

If lecture is removed from the classroom, then what should replace it? This is the question we faced this year when we put screencasts of our calculus lectures on YouTube at www.youtube.com/user/drprice765. In this talk we will discuss how we incorporated IBL techniques and transformed our traditional homework sets to create an active learning environment, in which students could openly discuss mathematics, compare and contrast ideas, and work together to solve problems.

We will have the participants cluster together into groups of five at the beginning of the talk, in order to simulate our classroom. Each cluster will watch a screencast and receive a packet comprised of three different problem sets (traditional, discussion-based, and theoretical) that were used to replace lecture.

Timothy Whittemore, Assessment Methods in IBL Courses

Abstract

This study seeks to investigate the practices instructors report using to assess
their students' learning and how these assessments affect the instruction in their
classrooms. Using data collected from 23 instructors using inquiry-based learning [IBL]
methods, I discuss the instructors' goals for the students, the ways they measured the
students' progress towards these goals, and the feedback they gave students. The
analysis of this data uses open coding of the transcripts, a coding of the documents
(e.g., syllabi, notes, homework assignments, exams) that the instructors gave to the
students, and an analysis of the online logs that the instructors completed to reflect on
their use of IBL methods. Findings suggest that instructors use both formative and
summative assessment methods, pay particular attention to both student-led
presentations and end of semester examinations, use assessment methods to aid the
students' learning of the material, and are uneasy about the need to grade students.

Nina White, Informal Student Presentations in IBL courses: to assess or not assess?

Abstract

In many IBL courses much of class time is spent on students making informal presentations of problems. The goal of this session is to discuss what role, if any, such presentations should play in the summative assessment of students. Further, if we choose to assess student presentations, what should be the foci of such assessments and how do we implement them in real time?

Participants will discuss some of the following questions:

(1) Why would we choose to asses or not assess informal student presentations in an IBL course?
(2) If we choose to assess, what do we focus our assessment on?
(3) How would these assessment goals vary by type of course?
(4) What are the challenges (and solutions!) to actually implementing such an assessment?

The main activity of the session will be to watch videos of student presentations in a variety of IBL courses, discuss features of student presentations, and to jointly create various "presentation rubrics" for different courses and to test them on the videos.

Kathi Crow, Using points to customize student participation

Abstract

In an inquiry based classroom, students have multiple opportunities to show their understanding of the material including presentations, written assignments, and exams. Some students are quick to prove theorems and thrive on presenting their work to their classmates while others take longer to fully engage with the content or are too shy to present often. A points-based grading system can provide the flexibility to grade some students more heavily on their presentations while allowing other students to exhibit their mastery of the material through exams.

In this talk, I'll give an overview of the system I use in my real analysis and abstract algebra courses. We'll then break into groups to create points-based system based on course goals and objectives.

Opportunities to learn mathematics are heavily influenced by the tasks in which learners are engaged and the way in which these tasks are implemented (e.g., Stein & Lane, 1996). IBL is one way to provide students with opportunities to engage in high-level thinking and reasoning. As such, educators who teach mathematics content courses for prospective teachers are faced with the challenge of designing and implementing meaningful IBL tasks that will help their students develop deep mathematical content knowledge (Watson & Mason, 2007).

The facilitators of this session are all university teacher educators who have been collaborating to develop meaningful mathematical tasks for prospective elementary teachers. In the session, we will describe our task design and modification cycle by sharing our work in modifying a fraction-comparison task from Investigations, a well-known elementary curriculum, and implementing it in our content courses for prospective elementary teachers. We will highlight how we used IBL in order to support our students' high-level thinking. Throughout the session, participants will be asked to think about aspects of our modification process, and how they could incorporate aspects of it into their own IBL-driven mathematics content courses.

Assessing students' learning in IBL courses includes, but is not limited to evaluation of students' development of content knowledge, of learning skills, and of habits of mind of the discipline. Tracking students' development of habits of mind may be difficult, and requires careful exploration. In our project, we focus on creativity as one of the important features of habits of mind for the mathematics discipline. When teaching, avoiding the acknowledgment of creativity may “cause them to give up the study of mathematics altogether” (Mann, 2005, p. 239). Furthermore, not exposing students to creative proofs or solutions to problems could lead them to believe that the study of mathematics is about procedures and recollections of a correct proof technique. Despite the importance of thinking creatively in mathematics, there currently is no assessment tool that measures students' mathematical creativity or their growth in thinking creatively with regards to proof. Our research group developed a creativity-in-proof rubric by aligning items from a creative thinking rubric (Rhodes, 2010) along with another rubric by Leikin (2009). Workshop attendees will use this rubric to assess students' proof processes captured by Livescribe pencast. Participants will be able to make suggestions for revisions to the rubric based on ideas presented.

Ali S. Shaqlaih, Inquiry Based Learning in Discrete Mathematics

Abstract

In this presentation, I will present some IBL activities that I implemented in a discrete mathematics course. A qualitative analysis of students' preference will be presented. Attendees will be engaged in a discussion regarding the students' achievement and the course assessment.

Bill McKenna, Working hard is better than “being smart”: Research and Incorporation of a Growth Model of Intelligence

Abstract

A person's belief about whether intelligence is a fixed quantity or an attribute that can grow holds major implications for persistence, learning, and achievement.
This session will begin with a short presentation on the history of the research and recent findings, and then move to a discussion on how beliefs about intelligence relate to IBL classroom practices.

In a recent large-scale project, teaching experiments based on learning progressions (a collection of activities that are inquiry-based science experiments) were developed focusing on the carbon cycle, water cycle, and biodiversity, each with a quantitative reasoning component. They have been implemented in middle and high school science classrooms across the country. I will share a snapshot of what these activities look like in the classroom, possibly including student work, video from the classroom implementation, interviews with students and/or teachers about their implementation and participation in the teaching experiments, and content assessment data from the students and/or teachers.
Last year, 16 middle and high school teachers participated in a case study to investigate the nature of the implementation of these teaching experiments. Their use of the materials varied as their needs dictated. We coded these classroom videos for eight Learning Progression Teaching Strategies, including 'Engage students in guided or open inquiry with authentic events and experiences.' We will encapsulate the process tools used in inquiry within this teaching strategy to give a picture of how this worked in these classrooms. In this talk, it is our intent to share a snapshot of something similar to IBL that is happening in science classrooms.

Jacqueline Jensen-Vallin, Grading in an IBL Course

Abstract

When I began using IBL more than a decade ago, I was concerned with how to assign grades to students in a student-centered course. What percent of the grade should be based on presentations? How can I grade presentations? How can I grade the course with most of the work being done at the board? In this talk, I will share successful (and not-so-successful) grading policies, including suggesting a rubric for grading presentations which has been helpful for me and well-accepted by my students.

Dan Goldner, Reading skills for IBL mathematics

Abstract

Many IBL classes require close and careful reading of problems and theorems. Students encounter clear, but terse writing that mixes new concepts and vocabulary with symbols and unfamiliar word order. Strategies developed for teaching academic reading across subjects can help both English Language Learners and native English speakers access and engage with IBL course notes, raising energy levels, productivity and enthusiasm in class.

Fundamental to the concept of "Social Justice Mathematics" (SJM) is the idea that mathematics can be used to better understand complex social, political, and economic in/justice issues, as well as the idea that mathematics can be better understood through the investigation of these social justice issues. Thus, there is a point of convergence in the recognition that the development of mathematical literacy–broadly conceived–and the cultivation of critical consciousness are both processes pursued through inquiry. In this presentation I'll elaborate on these ideas, talk about the ways in which an orientation to SJM can inform our work, and engage participants in the analysis of SJM activities to identify opportunities to leverage and honor their students' mathematical, community, and critical knowledge. Such engagement illustrates an image of inquiry that is expanded beyond the walls of classrooms to include opportunities for students to make sense of – and possibly influence – social, political, and economic dynamics in their own schools and communities and in the world around them.

Violeta Vasilevska, Engaging high school students in discovery

Abstract

In the last seven years I have been involved in various outreach programs and activities with high school students. In this talk I will present a few projects that I have used frequently in outreach setting. All activities that will be discussed are designed to engage high school students in hands-on, discovery based activities that spark their curiosity and show them that math is fun, interesting, and exciting. Each project is created as a guided discovery activity that leads students in discovering new mathematical truths using their previous knowledge. During the guided activities, students are prompted to discuss their findings with their group, to explain their findings, to ask questions, and to answer questions about their conjectures. The high school students are generally not asked to prove the conjectures but rather the emphasis is put on just discovery. Possible project topics that will be discussed include: coloring different surfaces, Hamiltonian circuits, graph coloring and origami, and truncated polyhedra.

Betty Love and Cindy Corritore, Using the flipped classroom for inquiry based learning

Abstract

The flipped classroom is one approach to implementing inquiry based learning and is becoming increasingly popular at all levels. In this presentation, we will discuss our experience in implementing the flipped classroom in university-level linear algebra and programming courses. We will explore several aspects of the flipped classroom including the following: (1) marketing - our approaches to "selling" students on the the flipped classroom concept, the pros and cons of no marketing at all; how is this influenced by the experience and confidence level of the instructor? (2) engaging students - our strategies have included paired problem-solving at the board, problem-solving in groups at tables, games, electronic polling with peer instruction and just-in-time teaching; and (3) assessment - we insisted that students prepare before coming to class by administering a short quiz either before class or during the first five minutes of class; we'll talk about the types of questions included and how we used the results.

Big data analytics uses computer algorithms to create and then sort into structured information data that is available from some measurement process. A measurement process imposes structure on the response of individuals to something. Our innovations include a topic enumeration of a “universe of discourse”. This enumeration then allows the individual to self-select elements from this universe of discourse, and to make written responses only involving elements that are self-selected. Hand written responses are used because our universe is that body of knowledge that has been selected by educators to be the core of K-16 mathematics training. The messaging of students, within a peer-to-peer social media, uses handwritten symbols needed to express concepts about functions, set theory, the real number line and geometry. A modified R L Moore learning methodology is then realized within a social media. The neuroscience associated with deep learning is integrated with both in-class activities as well as within the proposed social media.

We students witnessed fist hand one professor's journey in incorporating IBL into the calculus sequence. When she started to incorporate IBL strategies into teaching the calculus sequence, every year she taught a little differently, As she learned more about what worked and what did not work and gained ideas about better ways to use more student-centered strategies, her teaching style edged closer to the discovery end of the continuum and away from the lecture end. Each of us has experienced a different active calculus learning experience and each of us has a unique perspective on inquiry-based learning. We have seen IBL from a teacher just starting to implement student discovery in her calculus classes and we have seen IBL from the same teacher a few years later. We offer a students' perspective on inquiry-based learning and how it has impacted our understanding of calculus, our success in future coursework, our future teaching styles, our ideas on what it means to learn and teach mathematics, and even our career choices.

We will have a panel of four students who will begin by briefly sharing their experiences. The remainder of the time will engage the audience with a question/answer session for the panel of students.

A panel of students from an Introduction to Proof course taught using Inquiry Based Learning in Spring 2013 will share their perspectives on the effects the experience has had on subsequent courses in math and other disciplines. Students will briefly review the general design of the proofs course including depiction of a typical class session, and will discuss what they each perceive to be the primary benefits and challenges of being a student in an IBL course. The students will elaborate on how the proofs class has affected their thinking and performance in other courses throughout the year following the course.

9:45 – 10:55: General

Elizabeth Thoren, Inquiring Minds Want to Know (I)

Abstract

As educators, we are trying to change our students by equipping them to generate and explore novel questions after they leave our courses. And yet, we rarely think actively about the nature of the questions we expect students to generate and explore or how we will teach them to participate in this inquiry. We believe that the first step in helping our students develop this complex skill is to articulate a rich description of the skill in experts so that we may purposefully design our courses around reaching this goal. In part I, we will reflect on our own question-generating skills and begin classifying the questions experts ask when exploring new mathematical phenomena.

Participants will engage with a fertile mathematical phenomenon by generating a large number of questions they would explore about this phenomenon, share some of those questions, and work as a group on categorizing these questions into types of inquiry moves we make

Brian Katz, Inquiring Minds Want to Know (II)

Abstract

. In part II, we will think about the big phases of mathematical inquiry and how we might help students become aware of and use this structure. Part II is accessible without having attended part I, though we expect the two parts to enhance each other.

John W. Neuberger, Moore, Calculus and a Search for Research Mathematicians

Abstract

Moore had three highly related goals for his many calculus classes:
(1) To teach a good liberal arts course.
(2) To prepare his students well for courses using calculus.
(3) To search for research mathematicians.
I will try to describe how he routinely managed to achieve these goals.

Melissa Tolley, A Try and Re-Try of Class Flipping Calculus

Abstract

Flipping classrooms is becoming more and more popular, and proving to be very successful. As a first year instructor, I attempted to flip Calculus I. Here, I talk about my first and second attempts, discussing the successes and failures of each.

I will show participants a clip of the videos that I use for Calculus, and then do a mock "random day of calculus." This involves, a mini summary of the video, with questions to the students, then group work.

IBL Outreach at its best! A small group of like-minded mathematicians in Upstate New York started meeting for dinner and discussing IBL and its use in their classrooms. More nearby mathematicians were gaining interest, so what did they do? Apply for a grant to encourage more IBL use in local mathematics classrooms! Come find out about the process of applying for a large grant from the Education Advancement Foundation.

David A. Cusick, Breaking the Silence

Abstract

Why do students clam up? In a Psychology Today webpage, Preston Ni reports that fear of public speaking is the number-one fear in America, ranking above fear of death. Professor Ni adds further that this is a fear of emotional death, to be inflicted by audience rejection.

For 18 years my students have been speaking and putting problems on the board even though some students dislike it. Respecting the students and valuing their actions has repaid me with lively and productive classes.

Last year I began to present this problem and my solution. Partway through the talk I planned a pause for a few questions. The audience response was more than gratifying. The questions and answers consumed the entire time remaining. Now I'd like to tell the rest of the story and to hear the rest of the questions.

Professors R.L. Moore and H. S. Wall placed high importance on accuracy in the written and spoken word. There is no doubt that language plays a critical role in mathematics teaching. We will argue that educators should model the highest standards of correctness in inquiries presented to students; and we will demonstrate with real examples, that, sadly, this is not always done. Would you be shocked to learn that our children's high-stakes tests contain multiple-choice questions with no accurate answer choice provided? What are the consequences of giving students ambiguous or meaningless test questions? We will discuss these issues, and we will invite the participants to consider and evaluate actual samples at the secondary school level.

G. Edgar Parker, IBL Workshops

Abstract

In this talk, the presenter will discuss exercises he has used in conducting workshops with peers considering an interdisciplinary course, in-service teachers at both the secondary and elementary/middle school levels, and pre-service teachers. These exercises are designed to promote the possibilities for IBL.

Annie Selden and John Selden, What Kinds of Comments do Students make about Other Students' Proof Attempts?

Abstract

We report the results of a study of the proof validation abilities and behaviors of sixteen undergraduates after taking an inquiry-based transition-to-proof course. Students were interviewed individually towards the end of the course using the same protocol that we had used earlier at the beginning of a similar course (Selden and Selden, 2003). Results include a description of the students' observed validation behaviors, a description of their proffered evaluative comments, and the, perhaps counterintuitive, suggestion that taking an inquiry-based transition-to-proof course does not seem to enhance students' validation abilities. We also discuss distinctions between proof validation, proof comprehension, proof construction and proof evaluation and the need for research on their interrelation.

Algebraic topology is typically considered difficult to teach using a Moore method approach since it is heavily motivated by examples. This differs from the more axiomatic approach of general topology. For this reason there appears to be a clear division in teaching style when students familiar with learning from the viewpoint of Moore method begin a course in algebraic topology.

In the 1920s, Vietoris developed a homology theory for compact metric spaces. The subject of Vietoris homology, and subsequently simplicial and singular homology, was studied via inquiry by three advanced graduate students over the course of a semester.

Although algebraic topology can be difficult for the student to proceed via inquiry, without structured guidance, we will show how the inquiry based approach was used effectively in this course. By beginning with fundamental concepts of algebraic topology, and moving towards the more advanced theories, the students were able to build an intuition for the subject. This led to effective inquiries regarding some of the deeper aspects of the course. We will outline the theory behind the course and the methods used in the teaching.

11:20 – 12:20 IBL Episodes in K-12 Teacher Education and Professional Development, Dale Oliver. Available on YouTube at AcademyIBL